ABC limited expected to pay 18 dollars every year on a share of its stock. what is the present value of a share if money work is 9% compounded annually?
To find the present value of a share, we can use the formula for the present value of an ordinary annuity:
Present Value = Payment * (1 - (1 + r)^(-n)) / r
Where:
Payment = $18 (the payment per year)
r = 9% = 0.09 (the interest rate as a decimal)
n = 1 (the number of years)
Plugging in the values, the formula becomes:
Present Value = $18 * (1 - (1 + 0.09)^(-1)) / 0.09
Simplifying:
Present Value = $18 * (1 - (1.09)^(-1)) / 0.09
Present Value = $18 * (1 - 0.9174) / 0.09
Present Value = $18 * 0.0826 / 0.09
Present Value = $1.4828
Therefore, the present value of a share is approximately $1.48.
To calculate the present value of a share, we can use the formula for present value of an ordinary annuity:
Present Value = Payment / (1 + interest rate)^n
Where:
Payment = $18
Interest rate = 9% or 0.09
n = number of years (assume perpetuity, as it doesn't mention any specific time period)
Substituting the values:
Present Value = $18 / (1 + 0.09)^∞
Since the payment is expected to continue indefinitely, we consider it as a perpetuity, which means the present value formula becomes:
Present Value = Payment / interest rate
Present Value = $18 / 0.09 = $200
Therefore, the present value of a share is $200.
To find the present value of a share, we can use the formula for the present value of an annuity. The formula is:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present Value
PMT = Payment per period
r = Interest rate per period
n = Number of periods
In this case, ABC Limited is expected to pay 18 dollars every year and the interest rate is 9% compounded annually. We need to determine the present value of a share, which represents the total worth of all the future payments.
Using the formula mentioned above:
PMT = 18 dollars
r = 9% = 0.09
n = 1 (since it's compounded annually and we are given the payment per year)
Substituting the values into the formula:
PV = 18 * [(1 - (1 + 0.09)^(-1)) / 0.09]
Let's calculate it step by step:
1. Calculate the denominator:
(1 + 0.09)^(-1) = 1.09^(-1) = 0.9174
2. Calculate the difference: (1 - 0.9174) = 0.0826
3. Divide the difference by the interest rate:
0.0826 / 0.09 = 0.9174
4. Multiply the result by the payment per year:
18 * 0.9174 = 16.5126
Therefore, the present value of a share in ABC Limited is approximately 16.5126 dollars.